Curved surface processing method and curved surface processing apparatus

ABSTRACT

Disclosed are a curved surface processing method and a curved surface processing apparatus, which correct a relationship between a processing condition and a removal quantity (polished removal quantity) or a removal depth (polished removal depth) in accordance with a processed surface to obtain desired removal quantity or removal depth in processing a processed surface irrespective of the shape of the processed surface, form a reference surface in a simple shape to obtain the relationship between the processing condition and the removal quantity or the removal depth readily, and execute such correction of the relationship between the processing condition and the removal quantity or the removal depth and such correction of unit removal shapes readily for a short time.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a precision processingtechnology of a curved surface, which is capable of processing anoptical object or device including the curved surface and a metal moldfor molding the optical device precisely and efficiently while reducingvariations of the processing precision.

[0003] 2. Description of the Prior Art

[0004] As conventional precision processing technologies for a curvedsurface of an optical device, for example, there are the ones describedin the gazettes of Japanese Patent Laid-Open Nos. Hei 6 (1994)-170763,Hei 7 (1995)-68456 and Hei 11 (1999)-245152.

[0005] The technology described in the gazette of Japanese PatentLaid-Open No. Hei 6 (1994)-170763 is a polishing method capable ofexecuting a polishing step while automatically creating a polishingorbit in the same apparatus. In the polishing method, a measuring toolis attached to the processing apparatus, a polishing area of a work isdivided in two axial directions perpendicular to each other by aneffective radius unit where a polishing tool contacts the work, and withthus obtained divisional lines taken as a polishing pattern, thepolishing area is made to profile the pattern. Thus, impedance controlis carried out so that force detected by a force sensor can be a setvalue to obtain a position and data of a curved surface in anintersection point of the divisional lines. Thereafter, the polishingtool is attached, and based on the above-described curved surface data,a polishing route is decided, and thus the polishing is carried out bythe impedance control.

[0006] Moreover, the technology described in the gazette of JapanesePatent Laid-Open No. Hei 7 (1995)-68456 is a corrective polishingprocessing method capable of automating polishing processing for ahigh-precision metal mold, an aspheric lens and the like that is notaxially symmetric and of enhancing precision thereof. In the correctivepolishing processing method, a self-profile polishing apparatus and anautomatic measuring apparatus are disposed on a principal axis head of aNC machine tool controlled by a control apparatus, and measurement andcorrective polishing processing are performed for a surface of processedmatter. Then, during the measurement, a moving tolerance and a thermaldrift of the machine are corrected, an actual polished quantity per onepath is monitored based on a result of the measurement, and the nextpolished quantity is estimated based on this actual polished quantity,and the next polishing number is set. Simultaneously, in order toprevent overshoot due to variations of the polished quantity, acorrection coefficient is introduced.

[0007] Furthermore, the technology described in the gazette of JapanesePatent Laid-Open No. Hei 11 (1999)-245152 is a polishing apparatus forhigh-precision finish polishing for a surface shape of a surface of anoptical use and for achieving higher efficiency of the polishingprocessing for a curved surface of an optical object. The polishingapparatus for polishing the curved surface of a work attached to a worksupport tool, includes: a polishing head provided with a polisher in atip thereof, the polisher processing the optical curved surface of thework while rotating the same; a slider for pressing the polisher to anormal line direction to the curved surface, the slider having apolishing head disposed thereon; a motor rotating the polisher; a Z-axismechanism unit for moving the polisher provided in the polishing headdisposed in the slider so as to abut against or to be isolated from thecurved surface of the work; and a non-contact displacement meterattached to the polishing head and moving together with the polishinghead, wherein the curved surface is polished into a desired shape by thepolisher while a distance between the curved surface and the non-contactdisplacement meter being measured in a state where the polisher abutsagainst the curved surface.

[0008] Incidentally, heretofore, as an article processed to have acurved surface, a mirror for X-rays has been processed highly precisely.A final processing step for the mirror is polishing. The mirror forX-rays has a relatively large curvature radius, which is nearly a plane.On the other hand, in the case where a free curved surface of an devicein an optical field, a mold (or a piece of the mold) or the like ispolished precisely, which has a curvature radius smaller than that ofthe mirror for X-rays, it has been found out that there occurs a problemof a large tolerance of an actual removal depth with respect to a targetremoval depth if the curvature radius is reduced (a value of thecurvature is isolated from zero) as shown in FIG. 8. Note that, in FIG.8, a curvature of a convex surface is represented as positive, and acurvature of a concave surface is represented as negative.

[0009] Moreover, particularly in a free curved surface in which a largechange of the curvature radius such as a change from the convex surfaceto the concave surface is present, the above-described tolerance greatlyaffects the processing precision. Accordingly, it has been made apparentthat some correction is required in response to the curvature radius.Heretofore, a relationship between the removal depth and the processingcondition has been previously grasped, and the processing condition hasbeen set with respect to the target removal depth. However, therelationship described above has not been corrected in response to theshape of the processed surface, and particularly, to the curvatureradius.

[0010] The related art described in the foregoing gazette of JapanesePatent Laid-Open No. Hei 6 (1994)-170763 is an example of automaticallycreating the polishing orbit, where the correction for the shape has notbeen performed. Therefore, high-precision processing cannot beperformed.

[0011] Moreover, in the high-precision processing according to therelated art described in the foregoing gazette of Japanese PatentLaid-Open No. Hei 7 (1995)-68456, steps of measuring the shape,polishing the surface, measuring the shape, polishing the surface . . .are iterated plural times, whereby desired precision is achieved takinga long time. Also in this example, the correction for the curvatureradius is not performed.

[0012] Furthermore, the related art described in the foregoing gazetteof Japanese Patent Laid-Open No. Hei 11 (1999)-246152 is a method forcorrecting the position of the polishing head based on measurement dataobtained while measuring the distance between the processed surface andthe non-contact displacement meter moving together with the polishinghead. In this method, since the processed surface is contaminated bycuttings, abrasive grains or the like, the measuring precision haslimitations. Accordingly, the processing precision based on themeasurement result also has limitations naturally.

[0013] As described above, each of the related prior arts haslimitations in processing precision, and convergence of the processingprecision also has limitations. Therefore, each of the related arts isstill insufficient for realizing the high-precision processing whilereducing the variations of the processing precision as much as possible.

SUMMARY OF THE INVENTION

[0014] An object of the present invention is to realize a processingtechnology capable of polishing a free curved surface of an opticaldevice, a metal mold (metal piece) for molding the optical device or thelike highly precisely irrespective of a size of the curvature radius ofthe free curved surface.

[0015] Another object of the present invention is to complete the finishpolishing by performing one cycle of the steps of measuring the shape,polishing the surface and measuring the shape with regard to thehigh-precision polishing processing technology.

[0016] Still another object of the present invention is to realize aprinting apparatus capable of high-speed and high-definition printing,on which an optical device molded by use of the metal mold for theoptical device is mounted, the metal mold being obtained by the curvedsurface processing method and the curved surface processing apparatus ofthe present invention.

[0017] To accomplish the above objects, a first feature of the presentinvention is a curved surface processing method for processing a curvedsurface by applying a load between a tool and a processed surface, themethod comprising the steps of: grasping previously a relationshipbetween a processing condition and any of a removal quantity (an amountof removed powder or chips) and a removal depth (polished depth) byprocessing a reference surface of a same material as a material of anobjective processed surface prior to processing the objective processedsurface; correcting the relationship between the processing conditionand any of the removal quantity and the removal depth in the referencesurface in accordance with a shape of the processed surface; andprocessing the processed surface.

[0018] For the objective matter for polishing processing, information inthe polishing processing (information regarding such as the relationshipbetween the processing condition and the removal quantity or the removaldepth, which is grasped by processing the reference surface of thematerial as that of the processed surface) is grasped by actualprocessing. Based on the information, and the relationship between theprocessing condition and the removal quantity or the removal depth inthe reference surface is corrected in accordance with the shape of theprocessed surface, then the load, the tool peripheral velocity and thelike in the polishing processing are controlled. Thus, the processedsurface can be finished in high curved surface precision in onepolishing processing. Then, the control information is obtained for eachprocessed matter different in shape, and the polishing control isperformed similarly, thus making it possible to perform the polishingprocessing in similar precision irrespective of any shape of thepolished processed surface.

[0019] A second feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the reference surface is one or more of a plane, aspherical surface and a cylinder surface.

[0020] In the first feature of the present invention, the referencesurface is formed into a simple shape. Therefore, in the case where theremoval shape formed by the processing is measured and analyzed, whenthe reference surface is developed into a plane, it is not necessary tosubtract a complicated shape, but only a simple shape may be subtracted,and the reference surface can be readily developed into the plane.Accordingly, data of the removal quantity, the removal depth and theunit removal shape can be readily obtained. Therefore, the relationshipbetween the processing condition and the removal quantity or the removaldepth can be readily obtained.

[0021] Moreover, by forming the reference surface into the simple shape,a difference in shape between the actual processed surface and thereference surface can be obtained relatively readily, and the correctionfor the relationship between the processing condition and the removalquantity or the removal depth and the correction for the unit removalshape can be executed readily for a short time.

[0022] A third feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the shape of the processed surface is one obtained byindicating a cross-section of the processed surface by an approximatecurvature radius.

[0023] In the first feature of the present invention, the cross-sectionof the processed surface is indicated by the approximate curvatureradius, thus making it possible to indicate the shape of the processedsurface by a simple form. Accordingly, a difference in approximatecurvature radius between the processed surface and the reference surfacecan be simply obtained, and the relationship between the processingcondition and the removal quantity or the removal depth in the processedsurface can be corrected.

[0024] A fourth feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the shape of the processed surface is one obtained byindicating the cross-section of the processed surface by an approximatepolynomial.

[0025] In the first feature of the present invention, the cross-sectionof the processed surface is indicated by the approximate polynomial,thus making it possible to indicate the shape of the processed surface.Accordingly, a difference in approximate polynomial between theapproximate polynomial of the processed surface and approximatecurvature radius of the reference surface can be simply obtained, andthe relationship between the processing condition and the removalquantity or the removal depth in the processed surface can be corrected.

[0026] A fifth feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the shape of the processed surface is a shape of apartial processed surface in each area obtained by dividing theprocessed surface in a desired interval.

[0027] In the first feature of the present invention, the shape of theprocessed surface is the shape of the partial processed surface in eacharea obtained by dividing the processed surface in a desired interval.Therefore, the entire processed areas in the free curved surface wherethe approximate curvature radius or the approximate polynomial ischanged depending on the processed area can be divided in the desiredinterval to be indicated. Specifically, also for the free curved surfaceincapable of indicating the entire areas by the same approximatecurvature radius or the approximate polynomial like a spherical surfaceor a cylinder surface having a simple shape, the shape of the processedsurface can be indicated at a necessary level. Accordingly, in the freecurved surface, the relationship between the processing condition andthe removal quantity or the removal depth can be corrected in accordancewith the shape of the partial processed surface in each divisionalprocessed area.

[0028] A sixth feature of the present invention is the curved surfaceprocessing method according to the first feature of the presentinvention, wherein the shape of the processed surface is obtained basedon measurement data of the shape of the processed surface, themeasurement data being measured prior to polishing the shape of theprocessed surface.

[0029] In the first feature of the present invention, the shape of theprocessed surface is obtained based on the measurement data of the shapeof the processed surface, which is measured prior to polishing the shapeof the processed surface. Thus, the data for concretely indicating theshape of the processed surface can be obtained. Accordingly, the shapeof the processed surface for correcting the relationship between theprocessing condition and the removal quantity or the removal depth canbe obtained.

[0030] A seventh feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention 1, wherein the shape of the processed surface is obtainedbased on a predetermined design value.

[0031] In the first feature of the present invention, the shape of theprocessed surface is obtained based on the predetermined design valueprior to the polishing, whereby the data for concretely indicating theshape of the processed surface can be obtained. Accordingly, the shapeof the processed surface for correcting the relationship between theprocessing condition and the removal quantity or the removal depth canbe obtained.

[0032] An eighth of the present invention is a curved surface processingmethod according to the first feature of the present invention, whereinthe processing condition is a condition capable of changing any of theremoval quantity and the removal depth.

[0033] In the first feature of the present invention, the processingcondition is a condition capable of changing the removal quantity or theremoval depth. Therefore, a desired removal depth can be obtained ineach processed point by changing the condition in each processed point.

[0034] In the eighth feature of the present invention, the conditioncapable of changing the removal quantity or the removal depth is atleast one condition of the stay period, the tool peripheral velocity andthe load.

[0035] In the eighth feature of the present invention, since thecondition capable of changing the removal quantity or the removal depthis at least one condition of the stay period, the tool peripheralvelocity and the load, the removal quantity or the removal depth can bechanged readily, whereby the high-precision processing regarding theshape or the surge can be realized.

[0036] A ninth feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the reference surface of the same material as thematerial of the objective processed surface is processed prior toprocessing the objective processed surface to obtain unit removal shapesin the reference surface, and the unit removal shapes in the referencesurface are corrected in accordance with the shape of the processedsurface, then simulation of superposing the corrected unit removalshapes is carried out to correct the relationship between the processingcondition and any of the removal quantity and the removal depth inaccordance with the shape of the processed surface.

[0037] In the first feature of the present invention, the referencesurface of the same material as the material of the processed surface isprocessed prior to processing the objective processed surface to obtainunit removal shapes in the reference surface, and the unit removalshapes in the reference surface are corrected in accordance with theshape of the processed surface, then the simulation of superposing thecorrected unit removal shapes is carried out. Thus, based on thesimulation of superposing the corrected unit removal shapes, therelationship between the processing condition and the removal quantityor the removal depth can be corrected. Accordingly, the relationshipbetween the processing condition and the removal quantity or the removaldepth can be accurately corrected in accordance with the shape of theprocessed surface by the minimum processing experiment.

[0038] An tenth feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the reference surface of the same material as thematerial of the objective processed surface is processed prior toprocessing the objective processed surface to obtain unit removal shapesin the reference surface, and the unit removal shapes in the referencesurface are corrected in accordance with the shape of the processedsurface, then simulation of superposing the corrected unit removalshapes is carried out to calculate the processing condition.

[0039] In the first feature of the present invention, the referencesurface of the same material as the material of the objective processedsurface is processed prior to processing the objective processed surfaceto obtain unit removal shapes in the reference surface, and the unitremoval shapes in the reference surface are corrected in accordance withthe shape of the processed surface, then simulation of superposing thecorrected unit removal shapes is carried out to calculate the processingcondition. Thus, it is made possible to allow the shape obtained bysuperposing an enlarged or reduced unit removal shape in the depthdirection to coincide with a desired removal shape (or a tolerance froma desired shape) in a desired tolerance or less. Then, the processingcondition can be calculated corresponding to the above enlargement orreduction. Accordingly, the processing condition in accordance with theshape of the processed surface can be accurately calculated based on theminimum processing experiment.

[0040] An eleventh feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the shapes of the processed surface are obtained intwo directions perpendicular to each other, and the obtained shapes arecorrected.

[0041] In the first feature of the present invention, the shapes of theprocessed surface are obtained in two directions perpendicular to eachother, and the obtained shapes are corrected. Thus, the approximatecurvature radii or the approximate polynomials in the two perpendiculardirections on the processed surface can be obtained, and differences ofthe shapes in the two directions from the reference surface areobtained. Thus, the correction in accordance with the shape of theprocessed surface can be simply performed.

[0042] A twelfth feature of the present invention is a curved surfaceprocessing method according to the first feature of the presentinvention, wherein the shapes of the processed surface are obtained intwo directions perpendicular to each other, and one of the obtainedshapes having a smaller curvature radius is corrected.

[0043] In the first feature of the present invention, the shapes of theprocessed surface are obtained in two directions perpendicular to eachother, and one of the obtained shapes having a smaller curvature radiusis corrected. Then, the shape having the smaller curvature radiuslargely affects the removal quantity or the removal depth. Accordingly,since a larger effect is obtained when the shape having the smallercurvature radius is corrected, the correction in accordance with theshape of the processed surface can be simply performed by the correctionfor the shape in one direction.

[0044] A thirteenth feature of the present invention is a curved surfaceprocessing method according to the ninth or tenth feature of the presentinvention, wherein, when the processed surface is deformed to a sameshape as a shape of the reference surface, the unit removal shapes inthe reference surface are deformed in a same direction as a normal linedirection on a vertex of the processed surface and by a same distance asa moving distance thereof in the normal line direction to correct theunit removal shapes.

[0045] In the ninth or tenth feature of the present invention, when theprocessed surface is deformed to the same shape as that of the referencesurface, the unit removal shapes in the reference surface are deformedin the same direction as the normal line direction on the vertex of theprocessed surface and by the same distance as the moving distancethereof in the normal line direction to correct the unit removal shapes.Thus, based on the unit removal shapes obtained in the referencesurface, the corrected shape in accordance with the shape of theprocessed surface can be calculated in conformity with the above rule.By performing this calculation for each area of the processed surface,the unit removal shape in each processed surface can be obtained.

[0046] A fourteenth feature of the present invention is a curved surfaceprocessing method according to the ninth or tenth feature of the presentinvention, wherein the unit removal shapes are obtained by processing aprocessed surface of the same shape and material as the shape and thematerial of the processed surface to be processed.

[0047] In the ninth or tenth feature of the present invention, the unitremoval shapes are obtained by processing the processed surface of thesame shape and material as the shape and the material of the processedsurface to be processed. Thus, the data of the unit removal shapescorresponding to the processed surface can be accurately obtained, andthus the unit removal shape in each processed surface can be obtained.

[0048] A fifteenth feature of the present invention is any of a programin the curved surface processing method according to the ninth featureof the present invention and a storage medium having the program storedtherein, wherein the program allows a computer to function as means forcalculating the shape of the processed surface, means for correcting theunit removal shapes based on the calculated shape and means forsuperposing the corrected unit removal shapes to simulate therelationship between the processing condition and any of the removalquantity and the removal depth in accordance with the processed surface.

[0049] In the ninth feature of the present invention, in the program orthe storage medium having the program stored therein, the program allowsthe computer to function as means for calculating the shape of theprocessed surface, means for correcting the unit removal shapes based onthe calculated shape and means for superposing the corrected unitremoval shapes to simulate the relationship between the processingcondition and the removal quantity or the removal depth in accordancewith the processed surface. Therefore, by means of the program, theshape of the processed surface can be calculated, the unit removalshapes can be corrected, and the unit removal shapes can be superposed.Accordingly, the relationship between the processing condition and theremoval quantity or the removal depth in accordance with the processedsurface can be calculated automatically and rapidly.

[0050] A sixteenth feature of the present invention is any of a programin the curved surface processing method according to the tenth featureof the present invention and a storage medium having the program storedtherein, wherein the program allows a computer to function as means forcalculating the shape of the processed surface, means for correcting theunit removal shapes based on the calculated shape and means forsuperposing the corrected unit removal shapes to perform simulation furcalculating the processing condition.

[0051] In the tenth feature of the present invention, in the program orthe storage medium having the program stored therein, the program allowsthe computer to function as means for calculating the shape of theprocessed surface, means for correcting the unit removal shapes based onthe calculated shape and means for superposing the corrected unitremoval shapes to perform simulation for calculating the processingcondition. Therefore, by means of the program, the shape of theprocessed surface can be calculated, the unit removal shapes can becorrected, and the shape obtained by superposing an enlarged or reducedunit removal shape in the depth direction can be allowed to coincidewith a desired removal shape (or a tolerance from a desired shape) in adesired tolerance or less. Then, the processing condition can becalculated corresponding to the above enlargement or reduction.Accordingly, the processing condition in accordance with the processedcurved surface can be calculated automatically and rapidly.

[0052] A seventeenth feature of the present invention is a curvedsurface processing method according to any one of the first to sixteenthfeatures of the present invention, wherein a surge having a wave lengthof a contact width of the tool to the processed surface or larger isremoved by controlling the processing condition.

[0053] In the first to sixteenth features of the present invention, thesurge having the wavelength of the contact width of the tool to theprocessed surface or larger is removed by controlling the processingcondition. Thus, the surge data in the wavelength range of the contactwidth of the tool to the processed surface or larger can be taken out ofthe surge (tolerance) existing on the processed surface, and based onthe data, the removal depth in each processed point can be calculated.Then, by controlling the processing condition in accordance with theremoval depth, it is possible to positively remove the surge having thewavelength of the contact width of the tool to the processed surface,which cannot be removed in processing for obtaining an even removaldepth.

[0054] A eighteenth feature of the present invention is a curved surfaceprocessing apparatus in the curved surface processing method accordingto any one of the first to sixteenth features of the present invention,wherein a surge having a wavelength of a contact width of the tool tothe processed surface or larger is removed by controlling the processingcondition.

[0055] In the curved surface processing method according to the first tosixteenth features of the present invention, the surge having thewavelength of the contact width of the tool to the processed surface orlarger is removed by controlling the processing condition. Thus, thesurge data in the wavelength range of the contact width of the tool tothe processed surface or larger can be taken out of the surge(tolerance) existing on the processed surface, and based on the data,the removal depth in each processed point can be calculated. Then, bymeans of the curved surface processing apparatus capable of preciselycontrolling the processing condition in accordance with the removaldepth, it is possible to positively remove the surge having thewavelength of the contact width of the tool to the processed surface,which cannot be removed in processing for obtaining an even removaldepth.

[0056] A nineteenth feature of the present invention is a processedmatter processed by means of the curved surface processing methodaccording to any one of the first to eighteenth features of the presentinvention.

[0057] In this aspect, the processed matter is a metal mold for moldingan optical device.

[0058] A twentieth feature of the present invention is an optical devicemolded by use of the metal mold for the optical device according to theabove-described aspect.

[0059] Further, the present invention is characterized in that a curvedsurface processing apparatus comprises processing means for processing aprocessed surface, load-generating means for generating a load between atool and the processed surface, means for processing a reference surfaceof a same material as that of the processed surface is processed, priorto processing the objective processed surface to grasp previously therelationship between the processing condition and the removal quantityor the removal depth, and means for correcting the relationship betweenthe processing condition and the removal quantity or the removal depthin the reference surface to correct in accordance with the shape of theprocessed surface, then to process the processed surface.

[0060] The other objects, features and advantages of the presentinvention will be apparent from the following description made inconnection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0061]FIG. 1 is a front view schematically showing a whole of aprocessing apparatus of polishing processing for a curved surface.

[0062]FIG. 2 is a schematic view inflatedly showing a tolerance betweena desired designed shape and a measurement result of a shape of aprocessed surface before processing (concretely, before polishing).

[0063]FIG. 3 is a graph showing correction of a unit removal shape inEmbodiment 1.

[0064]FIG. 4 is a graph where corrected unit removal shapes aresuperposed.

[0065]FIG. 5 is a graph where uncorrected unit removal shapes aresuperposed.

[0066]FIG. 6 is a development view showing a tool path for a metal moldfor molding a long-scale optical device of Embodiment 2.

[0067]FIG. 7 is a view schematically showing coordinate positions ofthree points arrayed on a main bus-bar in an area 1 when curvature radiiwith respect to two directions of main and sub scanning directionsperpendicular to each other for an area divided into 40 sections in themain scanning direction are obtained by use of a computer.

[0068]FIG. 8 is a graph showing a relationship of an actual removaldepth to a target removal depth. FIG. 9 is an enlarged view of aprocessed cross-section.

[0069]FIG. 10 is an enlarged view schematically showing a state wherethe unit removal shapes are superposed in a method for obtaining aremoved quantity and a processing condition by superposing the unitremoval shapes.

[0070]FIG. 11 is a graph showing a relationship between each curvatureof the processed surface and a correction coefficient when the removaldepth is obtained by a function of a stay period.

[0071]FIG. 12 is a graph showing the relationship between each curvatureof the processed surface and the correction coefficient similarly toFIG. 11.

[0072]FIG. 13 is a graph of an example of correcting the unit removalshapes based on one example of the shapes of the processed surface inthe sub-scanning direction and the unit removal shape in a referencesurface (here, a plane).

[0073]FIG. 14 is a flowchart of a related art for a flowchart ofpolishing control of Embodiment 1 in FIG. 17.

[0074]FIG. 15 is a flowchart of a related art for a flowchart ofpolishing control of Embodiment 4 in FIG. 18.

[0075]FIG. 16 is a flowchart of a related art for a flowchart ofpolishing control of Embodiment 2 in FIG. 19.

[0076]FIG. 17 is a flowchart of the polishing control of Embodiment 1.

[0077]FIG. 18 is a flowchart of the polishing control of Embodiment 4.

[0078]FIG. 19 is a flowchart of the polishing control of Embodiment 2.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0079] Next, description will be made for embodiments with reference tothe drawings.

[0080] As shown in FIG. 1, a polishing processing apparatus is fixed toa spindle, in which a tool having a rotating tire shape or a rotatingspherical shape or alternatively having a shape composed of a part ofsuch shapes also serves as a direct moving slide. A specified load isgiven to the direct moving slide by a load generating mechanism unit,and the load is transmitted to the tool to generate a load (thrustforce) between the tool and a processed surface of processed matter. Theload is detected by a load sensor, and the load generating mechanismunit is controlled by an unillustrated control unit (for example, apersonal computer) so that the load can reach a specified value. Theprocessed matter can be subjected to so-called normal line control, inwhich a normal line of the processed surface is made to coincide with adirection where the load from the tool is loaded by an X-axis, a Y-axisand Z-axis and movements of a A-axis and a B-axis, which, are parallelto the X-axis and the Y-axis, respectively. When the processed surfaceis a plane, processing for the same as it is may be considered by thisnormal line control. On the other hand, when the processed surface is acurved surface, processing for a surface obtained by developing thecurved surface to an approximate plane may be considered. Here, a reasonwhy the “approximate plane” is mentioned is described as follows.Specifically, when the processed surface has a cylinder shapes, theprocessed surface can be developed into a plane. However, when theprocessed surface has other shapes, the processed surface cannot bedeveloped into a perfect plane, and the developed surface becomes anapproximate plane. In this case, a degree of developing a plane shouldbe examined and decided in accordance with a target precision.

[0081] As shown in FIG. 2, a tolerance exists between a desired designedshape of the processed surface and a measurement result of the shapethereof before processing (concretely, before polishing). Based on thetolerance, a removal quantity or a removal depth in each processingpoint is decided. Before processing the objective processed surface, aplane formed of the same material as that of this processed surface isprocessed, whereby a relationship between a processing condition and theremoval quantity or removal depth in the plane is grasped in advance,which is necessary. Regarding this relationship, heretofore, the Prestonrule represented by the following equation has been known.

δ=k×P×V×t

[0082] (δ: removal quantity, k: proportional constant, P: pressure, V:relative velocity of tool and processed point (tool peripheral velocity)and t: stay period)

[0083] In the present invention, δ may be regarded as a removal depth,and P may be regarded as the load described above. Specifically, k as aproportional constant will be obtained here, and there are the followingtwo methods for obtaining the proportional constant k.

[0084] One is a method for obtaining the proportional constant based onthe relationship between the removal depth and the processing condition,which is obtained when a sufficient area of a plane is processed withthe processing conditions other than the load, the relative velocity andthe stay period made constant. The other is a method for obtaining theremoval quantity and the processing condition by superposing unitremoval shapes, which are previously obtained as shapes obtained byprocessing the plane for a unit period, for example, one second, withthe processing conditions other than the stay period made constant.Here, the above “sufficient area” implies an area sufficient forobtaining a plane portion in a removal shape by processing as shown inFIG, 9. Moreover, superposing the unit removal shapes is referred to asa state shown in FIG. 10.

[0085] Based on the relationship between the removal depth and theprocessing condition, which is obtained as described above, theprocessing condition in each processed point is decided. Furthermore, inthe present invention, the relationship is corrected in response to theshape of the processed surface.

[0086] Although what will be a reference here is the relationshipbetween the processing condition and the removal quantity or depth inthe plane, an object thereof is not limited to a plane, and thereference may be a relationship therebetween in a curved surface havinga certain curvature radius.

EMBODIMENT 1

[0087] When a convex spherical surface having a curvature radius of 50mm is processed, a unit removal shape obtained by processing a plane,for example, a removal shape formed by thrusting a rotating tool againstthe plane for one second under a specified condition, is corrected tocope with the curvature radius of 50 mm. As shown in FIG. 3, the unitremoval shape is disposed so as to abut by vertex against the convexspherical surface having the curvature radius of 50 mm, and the unitremoval shape is deformed in the same direction as a vertical direction(normal direction) and by the same quantity as a moving quantity, thevertical direction and the moving quantity being observed when theconvex spherical surface is developed into a plane. A result obtained bysuch deformation is shown in a graph of a unit removal shape aftercorrection. An axis of ordinates indicates a depth of the removal shape,where a unit removal shape having a depth of about 6 μm is corrected toa unit removal shape having a depth of about 7 μm.

[0088]FIG. 4 shows a result of superposing the corrected unit removalshapes. The “superposing” mentioned here is arraying the corrected unitremoval shapes in a specified interval and integrating the unit removalshapes. The value obtained by such integration will be a removalquantity by the polishing processing. FIG. 4 is illustratedtwo-dimensionally for simplification. However, from FIG. 4, it isapparent that the result of such superposition is about 35 μm. In orderto obtain a removal quantity required for actual processing, forexample, a stay period is set for a fundamental processing conditionwhere the depth of about 35 μm is obtained, and thus the processingcondition will be decided. The relationship between the removal depthand the stay period is previously obtained, and the stay period and theremoval depth (removal quantity) are proportional to each other.Therefore, when the stay period is doubled, the removal depth will be 70μm. FIG. 5 shows a result of superposing uncorrected unit removalshapes. In this case, the removal depth is about 28 μm, causing atolerance of about 20% with respect to the removal depth under thefundamental processing condition. The unit removal shapes are correctedin response to the curvature radius of the processed surface, thusmaking it possible to decrease the tolerance.

[0089] A flowchart of Embodiment 1 is shown in FIG. 17, and a flowchartof the related art corresponding thereto is shown in FIG. 14. InEmbodiment 1, high-precision processing can be realized, and theprocessing is terminated in one cycle of measurement, polishing andmeasurement. However, it is not always necessary to terminate theprocessing in one cycle of the steps.

[0090] The above Embodiment 1 can be applied also when processing arotationally symmetric convex aspheric surface of an approximatecurvature radius of 50 mm. However, it is necessary to adjust Embodiment1 in accordance with degrees of an aspheric surface quantity and thetarget precision of the processed surface.

EMBODIMENT 2

[0091]FIG. 6 shows a metal mold for molding a long-scale optical device.In this case, processing is performed on a tool path as illustrated. Theprocessed surface is a free curved surface, where the curvature radiusis changed depending on a position of the processed surface. There is aprocessed area having a length of about 200 mm in the main scanningdirection and a length of about 3 mm in the sub-scanning direction. Thecurvature radii with respect to two directions of the main and subscanning directions perpendicular to each other for an area divided into40 sections in the main scanning direction are obtained by use of acomputer. Here, coordinates of three points arrayed on a main bus-bar inan area 1 shown in FIG. 7 are first calculated by use of the followingdesign equations.

(X1-a)²+(Z1-b)² =R ²  Equation (1)

(X2-a)²+(Z2-b)² =R ²  Equation (2)

(X3-a)²+(Z3-b)² =R ²  Equation (3)

[0092] where a and b are constants, R is a curvature radius,

b={(X1+X2)(X2−X3)(X1−X2)+(Z1+Z2)(Z1−Z2)(X2−X3)

−(X1−X2)(X2+X3)(X2−X3)−(X1−X2)(Z2+Z3)(Z2−Z3)}

/{2(Z1X2−Z1X3+Z2X3−Z2X1+Z3X1−Z3X2)}  Equation (4)

a={2b(−Z1+Z2)+(X1+X2)(X1−X2)+(Z1+Z2)(Z1−Z2)}

/{2(X1−X2)}  Equation (5)

[0093] As shown in FIG. 7, when (X1, Y1, Z1), (X2, Y2, Z2) and (X3, Y3,Z3) are the coordinates of the three points, a curvature radius of acircle passing through these three points is obtained by use ofEquations (1), (2) and (3). These three points are points apart from aleft end of the area 1 by 0.5 mm, 2.5 mm and 4.5 mm, respectively. Byuse of Equations (1), (2) and (3), the curvature radius R is obtained.Then, b is obtained by use of Equation (4), and a is obtained bysubstituting a value of b into Equation (5). Then, the curvature radiusR is obtained by substituting the values of a and b into Equation (1).Furthermore, determination is made as to whether the measured curvedsurface is a convex surface or a concave surface based on a positionalrelationship among the three points. Here, the curvature radius in themain scanning direction is obtained using the three points. However, themost fittable curvature radius way be obtained using points more thanthree by the least squared method. Moreover, a curvature radius in thesub-scanning direction, which passes through the point (X2, Y2, Z2), isobtained by use of a design equation, Thereafter, in a manner similar toEmbodiment 1, the unit removal shape is corrected with regard to themain scanning direction and the sub-scanning direction. Regarding thecorrected unit removal shape, two corrected removal shapes as shown inFIG. 3 are obtained with regard to the main and sub scanning directions.An average value thereof is adopted as the corrected unit removal shape.Also for other areas, the unit removal shapes are corrected in thesimilar manner. The unit removal depths of the unit removal shapes thusobtained are increased or decreased individually, followed bysuperposition thereof, and simulation is made so that a desired removalquantity can be obtained, and then, the stay periods are set in responseto the quantities increased or decreased individually. Besides the stayperiod, the tool peripheral velocity and the load can be also changed.

[0094] Here, the “desired removal quantity” is a tolerance between thedesired designed shape and the result of measuring the shape of theprocessed surface before the polishing as shown in FIG. 2. Since a widthin which the tool contacts the processed surface is 0.7 mm, the desiredremoval quantity is mentioned for a tolerance having a wavelength of 0.7mm or more.

[0095] A flowchart of Embodiment 2 is shown in FIG. 19, and a flowchartof the related art corresponding thereto is shown in FIG. 16. InEmbodiment 2, high-precision processing can be realized and theprocessing is terminated in one cycle of measurement, polishing andmeasurement.

EMBODIMENT 3

[0096]FIG. 6 shows the metal mold for molding the long-scale opticaldevice. In this case, processing is performed on the tool path asillustrated. The processed surface is a free curved surface, where thecurvature radius is changed depending on a position of the processedsurface. There is a processed area having a length of about 200 mm inthe main scanning direction and a length of about 3 mm in thesub-scanning direction. Simulation is carried out in such a manner thatthe curvature radii with respect to the two directions of the main andsub scanning directions perpendicular to each other for the area dividedinto 40 sections in the main scanning direction are obtained by use of acomputer. Here, the coordinates of three points arrayed on the mainbus-bar in the area 1 shown in FIG. 7 are first calculated by use of thedesign equations. As shown in FIG. 7, when (X1, Y1, Z1), (X2, Y2, Z2)and (X3, Y3, Z3) are the coordinates of the three points, the curvatureradius of the circle passing through these three points is obtained byuse of Equations (1), (2) and (3). These three points are points apartfrom the left end of the area 1 by 0.5 mm, 2.5 mm and 4.5 mm,respectively. By use of Equations (1), (2) and (3), the curvature radiusR is obtained, b is obtained by use of Equation (4), and a is obtainedby substituting a value of b into Equation (5). Then, the curvatureradius R is obtained by substituting the values of a and b into Equation(1). Furthermore, determination is made as to whether the measuredcurved surface is a convex surface or a concave surface based on thepositional relationship among the three points. Moreover, the curvatureradius in the sub-scanning direction, which passes through the point(X2, Y2, Z2), is obtained by use of a design equation. The correctedquantity of the unit removal shape is required more as the curvatureradius is smaller. Therefore, correction of the unit removal shape ismade for a smaller one of the curvature radii of the main and subscanning directions. Also for other areas, the unit removal shapes arecorrected in the similar manner. The unit removal depths of the unitremoval shapes thus obtained are increased or decreased individually,followed by superposition thereof, and simulation is made so that adesired removal quantity can be obtained, and then, the stay periods areset in response to the quantities increased or decreased individually.Besides the stay period, the tool peripheral velocity and the load canbe also changed. Here, the “desired removal quantity” is the tolerancebetween the desired designed shape and the result of measuring the shapeof the processed surface before the polishing as shown in FIG. 2. Sincethe width in which the tool contacts the processed surface is 0.7 mm,the desired removal quantity is mentioned for the tolerance having thewavelength of 0.7 mm or more. The shape of the processed surface ismeasured to analyze a surge having a wavelength ranging from 0.7 mm to 7mm. Consequently, a highly precise processed surface only with a surgehaving amplitude of 40 mm or less is obtained.

[0097] A flowchart of Embodiment 3 is shown in FIG. 19, and a flowchartof the related art corresponding thereto is shown in FIG. 16. InEmbodiment 3, high-precision processing can be realized, and theprocessing is terminated in one cycle of measurement, polishing andmeasurement.

EMBODIMENT 4

[0098]FIG. 6 shows the metal mold for molding the long-scale opticaldevice. In this embodiment, a material of the processed matter isstainless steel. The processing is performed on the tool path asillustrated. The processed surface is a free curved surface, where thecurvature radius is changed depending on a position of the processedsurface. There is a processed area having a length of about 150 mm inthe main scanning direction and a length of about 3 mm in thesub-scanning direction.

[0099] Prior to the processing, a plane formed of the same material asthat of the processed surface of the metal mold is processed, whereby arelationship between the removal depth and the processing condition isgrasped.

δ=200×t

[0100] (δ: removal depth (nm), t: stay period (sec/mm))

[0101] The above is the relationship between the removal depth and thestay period in the plane. Here, it is assumed that the tool peripheralvelocity and the load are constant, which are 20 mm/sec and 100 gf,respectively.

[0102] Moreover, changes of the removal depths with respect to thecurvature radius under the same processing conditions where the toolperipheral velocity is 20 mm/sec and the load is 100 gf when the stayperiod is 0.6 sec/mm are obtained from a processing experiment. Based ona result thereof, a correction coefficient C is obtained (FIG. 11). Withregard to the correction coefficient C, a relationship in the followingequation is established as also shown in FIG. 11.

δ=C×k×t

[0103] (δ: removal depth (nm), C: correction coefficient, k:proportional constant (200 in this embodiment), t: stay period (sec/mm))

[0104] As shown in FIG. 2, the removal depth of each processed point isobtained based on the tolerance between the desired designed shape andthe result of measuring the shape of the processed surface before thepolishing. Moreover, as shown in FIG. 7, the processed surface isdivided in the main scanning direction in an interval of 10 mm, and acurvature radius, that is, so-called a partial curvature radius isobtained based on the result of measuring the shape of each divisionalarea before the polishing. Based on the removal depth, the correctioncoefficient and the proportional constant in each processed point, thestay period as a processing condition can be obtained, and according tothis condition, the processing machine is controlled, and thus thehigh-precision polishing is executed.

[0105] Since the width in which the tool contacts the processed surfaceis 1 mm, a tolerance having a wavelength of 1 mm or more is set as anobject to be treated. Consequently, when the result of measuring theprocessed shape is analyzed for a surge having a wavelength ranging from1 mm to 10 mm, a highly precise processed surface only with a surgehaving amplitude of 30 mm or less is obtained.

[0106] A flowchart of Embodiment 4 is shown in FIG. 18, and a flowchartof the related art corresponding thereto is shown in FIG. 15. InEmbodiment 4, high-precision processing can be realized, and theprocessing is terminated in one cycle of measurement, polishing andmeasurement.

EMBODIMENT 5

[0107]FIG. 6 shows the metal mold for molding the long-scale opticaldevice. In this embodiment, a material of the processed matter is theone obtained by subjecting a stainless steel to non-electrolytic nickelplating. The processing is performed on the tool path as illustrated.

[0108] The processed surface is a free curved surface, where thecurvature radius is changed depending on a position of the processedsurface. There is a processed area having a length of about 170 mm inthe main scanning direction and a length of about 5 mm in thesub-scanning direction. This is a metal mold having a concave shapewhere the curvature radius in the sub-scanning direction is continuouslychanged from 30 mm to 85 mm depending on spots.

[0109] Prior to the polishing processing, processing is made for aconcave cylinder surface formed of the same material as that of theprocessed surface of the metal mold, the concave cylinder having acurvature radius of 50 mm, whereby the unit removal shape is obtained.Simulation of superposing the unit removal shapes is carried out,whereby the relationship between the removal depth and the processingcondition is grasped.

δ=300×t

[0110] (δ: removal depth (nm), t: stay period (sec/mm))

[0111] The above is the relationship between the removal depth and thestay period in the reference surface. Here, it is assumed that the toolperipheral velocity and the load are constant, which are 300 mm/sec and150 gf, respectively.

[0112] Moreover, the unit removal shapes on the concave cylindersurfaces, each having a curvature radius selected from 30 mm, 40 mm, 60mm and 80 mm, under the same processing conditions where the toolperipheral velocity is 300 mm/sec and the load is 150 gf when the stayperiod is 0.6 sec/mm are obtained from a processing experiment. Thesimulation for superposing the unit removal shapes is carried out,whereby the removal depths in the respective curvature radii areobtained. Based on a result thereof, a correction coefficient C isobtained (FIG. 12). FIG. 12 shows a relationship between the correctioncoefficient and a curvature as an inverse number of the curvature radiustaken as an axis of abscissas, where the concave surface is defined asnegative. Here, since the concave cylinder surface having the curvatureradius of 50 mm is taken as the reference surface, the correctioncoefficient becomes 1 when the curvature is −0.02/mm. With regard to thecorrection coefficient C, a relationship in the following equation isestablished as also shown in FIG. 12.

δ=C×k×t

[0113] (δ: removal depth (nm), C: correction coefficient, k:proportional constant (300 in this embodiment), t: stay period (sec/mm))

[0114] As shown in FIG. 2, the removal depth of each processed point isobtained based on the tolerance between the desired designed shape andthe result of measuring the shape of the processed surface before thepolishing. Moreover, the processed surface is divided in the mainscanning direction in an interval of 1 mm, and an approximate curvatureradius in the sub-scanning direction is obtained based on the result ofmeasuring the shape of each divisional area before the polishing. Basedon the removal depth, the correction coefficient and the proportionalconstant in each processed point, the stay period as a processingcondition can be obtained, and according to this condition, theprocessing machine is controlled, and thus the high-precision polishingis executed. Since the width in which the tool contacts the processedsurface is 1 mm, the tolerance having a wavelength of 1 mm or more isset as an object to be treated. Consequently, when the result ofmeasuring the processed shape is analyzed for a surge having awavelength ranging from 1 mm to 10 mm, a highly precise processedsurface only with a surge having amplitude of 30 nm or less is obtained.

[0115] A flowchart of Embodiment 5 is shown in FIG. 18, and a flowchartof the related art corresponding thereto is shown in FIG. 15. InEmbodiment 5, high-precision processing can be realized, and theprocessing is terminated in one cycle of measurement, polishing andmeasurement.

EMBODIMENT 6

[0116]FIG. 6 shows the metal mold for molding the optical device. Theprocessing is performed on the tool path as illustrated. The processedsurface is a free curved surface. When the approximate curvature radiiof the respective shapes in the main and sub scanning directions arecompared with each other, the approximate curvature radius of the shapein the sub-scanning direction is smaller. Therefore, the correction ismade in accordance with the shape in the sub-scanning direction. FIG. 13shows an example where the unit removal shape is corrected based on oneexample of the shape of the processed surface in the sub-scanningdirection and the unit removal shape on the reference surface (here, aplane). In this example, the shape of the processed surface obtained bymeasuring the processed surface is made approximate to the followingpolynomial,

Y=(1E−10)X2−(5E−20)X2−5

[0117] The unit removal shape is deformed in the normal line directionon the vertex when the above-described processed surface is deformed toa plane as the reference surface, that is, in the same direction as avertical direction of a moving quantity in FIG. 13 and by the samequantity as the moving quantity. Thus, the corrected unit removal shapesare obtained. By superposing the corrected unit removal shapes, thecorrected quantity in the shape of the processed surface is obtained,and the stay period is decided. Since the width in which the toolcontacts the processed surface is 1 mm, the stay period on eachprocessed point is set with the tolerance having a wavelength of 1 mm ormore taken as an object, and then the polishing is executed.Consequently, when the result of measuring the processed shape isanalyzed for a surge having a wavelength ranging from 1 mm to 10 mm, ahighly precise processed surface only with a surge having amplitude of30 nm or less is obtained.

[0118] A flowchart of Embodiment 6 is shown in FIG. 17, and a flowchartof the related art corresponding thereto is shown in FIG. 14. InEmbodiment 6, high-precision processing can be realized, and theprocessing is terminated in one cycle of measurement, polishing andmeasurement.

[0119] A high-precision optical device is molded by use of a metal moldprocessed as described above, from which the tolerance such as a surgeis removed. By means of a printing processing apparatus having theoptical device mounted thereon, high-speed and high-definition printingis enabled.

[0120] Effects of the present invention described above will besummarized as below.

[0121] (1) In processing of the curved surface by applying the loadbetween the tool and the processed surface, prior to processing theobjective processed surface, the reference surface of the same materialas that of the processed surface is processed to previously grasp therelationship between the processing condition and the removal quantityor the removal depth, and in accordance with the shape of the processedsurface the relationship between the processing condition and theremoval quantity or the removal depth in the reference surface iscorrected, then the processed surface is processed. Therefore, in thepolishing processing, desired removal quantity or removal depth can beobtained irrespective of the shape of the processed surface, thus makingit possible to realize the high-precision processing. Since thehigh-precision processing can be realized, it is not necessary toiterate the steps of measuring the shape, polishing the surface andmeasuring the shape, and the polishing finish is completed in onepolishing processing. The high-precision processed surface is obtainedfor a short time without iterating the polishing processing, and theobtained processed surface has a surge of several ten nm or less inprecision.

[0122] (2) The reference surface is one or more of a plane, a sphericalsurface and a cylinder surface. Therefore, by forming the referencesurface into a simple shape, acquisition of data thereof is facilitated,and correction of the unit removal quantity is also facilitated, thusmaking it possible to readily obtain the relationship between theprocessing condition and the removal quantity or the removal depth, andpossible to execute the correction of the relationship between theprocessing condition and the removal quantity or the removal depth andthe correction of the unit removal shapes for a short time.

[0123] (3) As the shape of the processed surface, the cross-section ofthe processed surface is indicated by the approximate curvature radius.Therefore, the relationship between the processing condition and theremoval quantity or the removal depth in the plane is corrected inaccordance with the approximate curvature radius, whereby thehigh-precision processing can be realized.

[0124] (4) As the shape of the processed surface, the cross-section ofthe processed surface is indicated by an approximate polynomial.Therefore, the relationship between the processing condition and theremoval quantity or the removal depth in the plane is corrected inaccordance with the approximate polynomial, whereby the high-precisionprocessing can be realized,

[0125] (5) The shape of the processed surface is a shape of a partialprocessed surface in each area obtained by dividing the processedsurface in a desired interval. Therefore, in the free curved surfacewhere the approximate curvature radius or the approximate polynomial ofthe processed surface changes depending on the processed area, therelationship between the processing condition and the removal quantityor the removal depth in the reference surface can be corrected inaccordance with the shape of the partial processed surface of each area,whereby the high-precision processing can be realized also in the freecurved surface.

[0126] (6) The shape of the processed surface is obtained based onmeasurement data of the shape of the processed surface, which ismeasured prior to polishing the shape of the processed surface.Alternatively, the shape of the processed surface is obtained based on apredetermined design value. Therefore, the shape of the processedsurface for correcting the relationship between the processing conditionand the removal quantity or the removal depth can be obtained, thusmaking it possible to execute the correction in each processed surface.

[0127] (7) The processing condition is a condition capable of changingthe removal quantity or the removal depth. Therefore, the removalquantity or the removal depth can be changed by the processing conditionin accordance with the necessary removal depth, whereby thehigh-precision processing regarding the shape or the surge can berealized.

[0128] (8) The condition capable of changing the removal quantity or theremoval depth is at least one condition of the stay period, the toolperipheral velocity and the load. Therefore, the removal quantity or theremoval depth can be changed readily, whereby the high-precisionprocessing regarding the shape or the surge can be realized.

[0129] (9) The reference surface of the same material as that of theobjective processed surface is processed prior to processing theobjective processed surface to obtain the unit removal shapes in thereference surface, and the unit removal shapes in the reference surfaceare corrected in accordance with the shape of the processed surface,then simulation of superposing the corrected unit removal shapes iscarried out. Therefore, the relationship between the processingcondition and the removal quantity or the removal depth can be correctedin accordance with the shape of the processed surface, thus making itpossible to accurately correct the relationship between the processingcondition and the removal quantity or the removal depth by the minimumprocessing experiment in accordance with the shape of the processedsurface. Moreover, a processing experiment for acquiring data of theunit removal shape corresponding to each processed surface shape is notperformed to reduce a period, electric power, a ground material,abrasive grains, lubrication oil and the like, which are required in thecase of performing the experiment, thus making it possible to decreasean environmental load.

[0130] (10) The reference surface of the same material as that of theobjective processed surface is processed prior to processing theobjective processed surface to obtain the unit removal shapes in thereference surface, and the unit removal shapes in the reference surfaceare corrected in accordance with the shape of the processed surface,then simulation of superposing the corrected unit removal shapes iscarried out. Therefore, the processing condition is calculated, thusmaking it possible to accurately calculate the processing condition inaccordance with the shape of the processed surface by the minimumprocessing experiment. Moreover, the processing experiment for acquiringthe data of the unit removal shape corresponding to each processedsurface shape is not performed to reduce the period, the electric power,the ground material, the abrasive grains, the lubrication oil and thelike, which are required in the case of performing the experiment, thusmaking it possible to decrease the environmental load.

[0131] (11) The shapes of the processed surface are obtained in twodirections perpendicular to each other, and the obtained shapes arecorrected. Therefore, the correction in accordance with the processedsurface can be simply performed.

[0132] (12) The shapes of the processed surface are obtained in the twodirections perpendicular to each other, and one of the obtained shapeshaving a smaller curvature radius is corrected. Therefore, thecorrection in accordance with the shape of the processed surface isperformed for the shape having the smaller curvature radius, whichaffects the removal depth more, whereby the correction can be performedsimply and effectively.

[0133] (13) When the processed surface is deformed to the same shape asthat of the reference surface, the unit removal shapes in the referencesurface are deformed in the same direction as a normal line direction ona vertex of the processed surface and by the same distance as a movingdistance thereof in the normal line direction to correct the unitremoval shapes. Therefore, it is made possible to obtain the unitremoval shape in each processed surface by calculation. Moreover, theprocessing experiment for acquiring the data of the unit removal shapecorresponding to each processed surface shape is not performed to reducethe period, the electric power, the ground material, the abrasivegrains, the lubrication oil and the like, which are required in the caseof performing the experiment, thus making it possible to decrease theenvironmental load.

[0134] (14) The shape of the processed surface is the shape of thepartial processed surface in each area obtained by dividing theprocessed surface in a desired interval. Therefore, it is made possibleto obtain the unit removal shape in each processed surface by theprocessing experiment, and more accurate unit removal shapes can beobtained for a ground material subjected to the processing little.

[0135] (16) There is provided a program allowing a computer to functionas means for calculating the shape of the processed surface, means forcorrecting the unit removal shapes based on the calculated shape andmeans for superposing the corrected unit removal shapes to simulate therelationship between the processing condition and the removal quantityor the removal depth in accordance with the processed surface.Alternatively, there is provided a storage medium, in which the programis stored. Therefore, it is made possible to calculate the relationshipbetween the processing condition and the removal quantity or the removaldepth in accordance with the processed surface automatically andrapidly, whereby it is made possible to set the processing condition ineach processed point, and the high-precision processing can be realized.

[0136] (16) There is provided a program allowing a computer to functionas means for calculating the shape of the processed surface, means forcorrecting the unit removal shapes based on the calculated shape andmeans for superposing the corrected unit removal shapes to performsimulation for calculating the processing condition. Alternatively,there is provided a storage medium, in which the program is stored.Therefore, it is made possible to calculate the processing condition inaccordance with the processed surface automatically and rapidly.Furthermore, the processing can be executed under the processingcondition, and the high-precision processing can be realized.

[0137] (17) There is provided the curved surface processing method, inwhich a surge having a wavelength of a contact width of the tool to theprocessed surface or larger is removed by controlling the processingcondition. Alternatively, there is provided a curved surface processingapparatus, in which a surge having a wavelength of a contact width ofthe tool to the processed surface or larger is removed by controllingthe processing condition. Therefore, it is made possible to positivelyremove the surge having the wavelength of the contact width of the toolto the processed surface, which cannot be removed in processing forobtaining an even removal depth, whereby surge precision in a desiredwavelength range can be improved.

[0138] (18) There is provided processed matter processed by means of acurved surface processing method. Therefore, the processed matter is theone from which the tolerance for the designed shape is removed, and itis possible to realize a desired optical function.

[0139] (19) The processed matter is a metal mold for molding an opticaldevice. Therefore, it is possible to obtain a metal mold for molding anoptical device, from which the tolerance for the designed shape isremoved, whereby a high-performance optical device can be obtained.

[0140] (20) There is provided an optical device molded by use of themetal mold for an optical device. Therefore, the high-performanceoptical device can be obtained, thus making it possible to obtain ahigh-performance printing processing apparatus.

[0141] Note that, when mounting the optical device as an optical deviceof the printing processing apparatus, since the optical device hasextremely high performance, high-speed and high-definition printing forcharacters and images can be made.

What is claimed is:
 1. A curved surface processing method for processinga curved surface by applying a load between a tool and a processedsurface, the method comprising steps of: grasping previously arelationship between a processing condition and any of a removalquantity and a removal depth by processing a reference surface of a samematerial as a material of an objective processed surface prior toprocessing the objective processed surface; correcting the relationshipbetween the processing condition and any of the removal quantity and theremoval depth in the reference surface in accordance with a shape of theprocessed surface; and processing the processed surface.
 2. The curvedsurface processing method according to claim 1, wherein the referencesurface is one or more of a plane, a spherical surface and a cylindersurface.
 3. The curved surface processing method according to claim 1,wherein the shape of the processed surface is one obtained by indicatinga cross-section of the processed surface by an approximate curvatureradius.
 4. The curved surface processing method according to claim 1,wherein the shape of the processed surface is one obtained by indicatingthe cross-section of the processed surface by an approximate polynomial.5. The curved surface processing method according to claim 1, whereinthe shape of the processed surface is a shape of a partial processedsurface in each area obtained by dividing the processed surface in adesired interval.
 6. The curved surface processing method according toclaim 1, wherein the shape of the processed surface is obtained based onmeasurement data of the shape of the processed surface, the measurementdata being measured prior to polishing the shape of the processedsurface.
 7. The curved surface processing method according to claim 1,wherein the shape of the processed surface is obtained based on apredetermined design value.
 8. The curved surface processing methodaccording to claim 1, wherein the processing condition is a conditioncapable of changing any of the removal quantity and the removal depth.9. The curved surface processing method according to claim 8, whereinthe condition capable of changing any of the removal quantity and theremoval depth is at least one condition of a stay period, a toolperipheral velocity and a load.
 10. The curved surface processing methodaccording to claim 1, wherein the reference surface of the same materialas the material of the objective processed surface is processed prior toprocessing the objective processed surface to obtain unit removal shapesin the reference surface, and the unit removal shapes in the referencesurface are corrected in accordance with the shape of the processedsurface, then simulation of superposing the corrected unit removalshapes is carried out to correct the relationship between the processingcondition and any of the removal quantity and the removal depth inaccordance with the shape of the processed surface.
 11. The curvedsurface processing method according to claim 1, wherein the referencesurface of the same material as the material of the objective processedsurface is processed prior to processing the objective processed surfaceto obtain unit removal shapes in the reference surface, and the unitremoval shapes in the reference surface are corrected in accordance withthe shape of the processed surface, then simulation of superposing thecorrected unit removal shapes is carried out to calculate the processingcondition.
 12. The curved surface processing method according to claim1, wherein the shapes of the processed surface are obtained in twodirections perpendicular to each other, and the obtained shapes arecorrected.
 13. The curved surface processing method according to claim1, wherein the shapes of the processed surface are obtained in twodirections perpendicular to each other, and one of the obtained shapeshaving a smaller curvature radius is corrected.
 14. The curved surfaceprocessing method according to any one of claims 10 and 11, wherein,when the processed surface is deformed to a same shape as a shape of thereference surface, the unit removal shapes in the reference surface aredeformed in a same direction as a normal line direction on a vertex ofthe processed surface and by a same distance as a moving distancethereof in the normal line direction to correct the unit removal shapes.15. The curved surface processing method according to any one of claims10 and 11, wherein the unit removal shapes are obtained by processing aprocessed surface of same shape and material as the shape and thematerial of the processed surface to be processed.
 16. A storage mediumin the curved surface processing method according to claim 10, whereinit stores a program that a computer is functioned as means forcalculating the shape of the processed surface, means for correcting theunit removal shapes based on the calculated shape and means forsuperposing the corrected unit removal shapes to simulate therelationship between the processing condition and any of the removalquantity and the removal depth in accordance with the processed surface.17. A program in the curved surface processing method according to claim10, wherein a computer is functioned as means for calculating the shapeof the processed surface, means for correcting the unit removal shapesbased on the calculated shape and means for superposing the correctedunit removal shapes to simulate the relationship between the processingcondition and any of the removal quantity and the removal depth inaccordance with the processed surface.
 18. A program in the curvedsurface processing method according to claim 11, wherein a computer isfunctioned as means for calculating the shape of the processed surface,means for correcting the unit removal shapes based on the calculatedshape and means for superposing the corrected unit removal shapes toperform simulation for calculating the processing condition.
 19. Astorage medium in the curved surface processing method according toclaim 11, wherein it stores a program that a computer is functioned asmeans for calculating the shape of the processed surface, means forcorrecting the unit removal shapes based on the calculated shape andmeans for superposing the corrected unit removal shapes to performsimulation for calculating the processing condition.
 20. The curvedsurface processing method according to any one of claims 1 to 15,wherein a surge having a wavelength of a contact width of the tool tothe processed surface or larger is removed by controlling the processingcondition.
 21. A curved surface processing method according to any oneof claims 1 to 15, wherein a surge having a wavelength of a contactwidth of the tool to the processed surface or larger is removed bycontrolling the processing condition.
 22. Processed matter, wherein theprocessed matter is processed by means of the curved surface processingmethod to any one of claims 1 to
 15. 23. The processed matter accordingto claim 22, wherein the processed matter is a metal mold for molding anoptical device.
 24. An optical device, wherein the optical device ismolded by use of the metal mold for an optical device of claim
 28. 25. Acurved surface processing apparatus comprising: processing means forprocessing a processed surface; load-generating means for generating aload between a tool and the processed surface; means for processing areference surface of a same material as that of the processed surface isprocessed, prior to processing the objective processed surface to grasppreviously the relationship between the processing condition and theremoval quantity or the removal depth; and means for correcting therelationship between the processing condition and the removal quantityor the removal depth in the reference surface to correct in accordancewith the shape of the processed surface, then to process the processedsurface.